1. Field of the Invention
The invention relates to the field of modeling field-effect transistors.
2. Prior Art
There is a growing need to provide optimal designs for integrated circuits particularly as the critical dimensions decrease and speed of such circuits increase.
A relatively recent development in mathematics has provided an improved computerated tool for designing integrated circuits using geometric programs. In general, an operating model is developed in the form of a posynomial function. The geometric program once in the form of a convex program can be solved with efficient interior-point methods. The most important feature of geometric programs is that they can be globally solved with great efficiency. The algorithm determines whether the problem is infeasible (i.e., no design can meet all constraints). Also, the starting point of an optimization algorithm does not have any affect on the solution.
One interior-point method is described by K. O. Kortanek, X. Xu, and Y. Ye, xe2x80x9cAn Infeasible Interior-point Algorithm for Solving Primal and Dual Geometric Programs,xe2x80x9d MathProgramming, 76:155-181, 1996. This method has the desirable feature of exploiting sparsity in the problem, (i.e., efficiently handling problems in which each variable appears in only a few constraints). Additional methods of solving geometric programs are described in: Y. Nesterov and A. Nemirovsky, xe2x80x9cInterior-Point Polynomial Methods in Convex Programming,xe2x80x9d Volume 13 of Studies in Applied Mathematics, SIAM, Philadelphia, Pa., 1994; and A. Fiacco and G. McCormick, NonlinearProgramming: Sequential Unconstrained Minimization Technologies, Wiley 1968 (Reprinted in SIAM Classics in Applied Mathematics series 1990).
The present invention is directed towards obtaining a posynomial expression for field-effect transistor model when operating in its saturation region. While numerous techniques are well known for obtaining mathematical expressions representing transistor characteristics including the operation of a transistor in its saturation region, these approaches do not necessarily lead to a posynomial expression useful in a geometric program.
The use of posynomial and monomial expression for circuits and their solution with geometric programs is discussed in Ser. No. 09/123,129, filed Jul. 27, 1998, entitled xe2x80x9cSystem and Method for Designing Integrated Circuits,xe2x80x9d now U.S. Pat. No. 6,269,277 and Ser. No. 09/335,227, filed Jun. 17, 1999, entitled xe2x80x9cOptimal Design of an Inductor and Inductor Circuitxe2x80x9d; now U.S. Pat. No. 6,311,145, both assigned to the assignee of this application.